2687: Division Notation

Explain xkcd: It's 'cause you're dumb.
Revision as of 00:49, 20 October 2022 by 172.70.230.105 (talk) ("English-speaking countries" changed to "some countries" as some non-English speaking countries use the long division symbol as well.)
Jump to: navigation, search
Division Notation
Science tip: Scientists hardly ever use the two-dot division sign, and when they do it often doesn't even mean division, but they still get REALLY mad when you repurpose it to write stuff like SALE! ALL SHOES 30÷ OFF!
Title text: Science tip: Scientists hardly ever use the two-dot division sign, and when they do it often doesn't even mean division, but they still get REALLY mad when you repurpose it to write stuff like SALE! ALL SHOES 30÷ OFF!

Explanation

Ambox notice.png This explanation may be incomplete or incorrect: Created by a GROUP OF SCHOOLCHILDREN DIVIDED AMONGST THEMSELVES - Please change this comment when editing this page. Do NOT delete this tag too soon.
If you can address this issue, please edit the page! Thanks.

This comic pokes fun at some of the ways to write the division operation in math. In this comic, Randall has used A as the dividend (the number being divided) and B as the divisor (the number that A is divided by).

The first two are respectively the division sign (÷) and long division symbol. (Note: the long division symbol is only used in some countries). These methods of division are often used by school children as the first ÷ is what people learn when first learning division, and the second long division symbol is usually the first type of long division learned (it's easier to do it visually on paper that way).

The third line is the way the division is often written in software code. The 4 standard operations in programming usually are +, -, *, /. This one was missing in the first version of the comic. This is most commonly seen in regular mathematics as it somewhat saves space, and is easy to type with the slash key.

The fourth notation is the way division is written in science, dividend on top line and divided on bottom line. This is the closest format to how a fraction would be written. This format would likely only be used in written math, as typing the fraction symbol requires the math markup language.

The fifth notation uses a negative exponent. The exponent -1 has the same effect as dividing by the base. It can be used to keep an equation on 1 line.

The final form of notation appears to be not a simple notation for division. Rather, it looks like a definition of a notion of division which is customized to a particular setting. This situation is likely to occur in abstract algebra, where one might have to define what "division" might mean for two elements of a mathematical object such as a group, ring, or magma. One example would be an object G, such that, for two elements A and B of G, "A divided by B" is defined as an element C such that CB=A, or alternatively as an element C such that BC=A. These definitions might differ if multiplication in G is not commutative. Furthermore, if such a C is not unique, a function F(A,B) might have to be chosen to select a unique value for "A divided by B" for each A and B. Thus, the F(A,B) in the comic might not even refer to a uniquely defined operation, but simply to the property of a function F(A,B) that is a valid division operation on G, given some definition of division.

Transcript

Ambox notice.png This transcript is incomplete. Please help editing it! Thanks.
Division notation
A÷B
B⟌A Schoolchild.
A/B Software engineer.
AB Normal person or Unicode enthusiast.
A over B Scientist.
AB-1 Fancy scientist.
F(A, B) such that F(G)= (text getting smaller) Oh no, run


comment.png add a comment! ⋅ comment.png add a topic (use sparingly)! ⋅ Icons-mini-action refresh blue.gif refresh comments!

Discussion

Fun fact: In Poland, we don't write the long division like that; we just write A:B with the bar above. I was VERY confused the first time I saw that notation. 172.70.246.235 21:03, 19 October 2022 (UTC)

Unrelated to Polish notation, i presume? 172.70.134.13 22:43, 19 October 2022 (UTC)Bumpf
Unrelated. Never used Polish notation in school. 172.71.160.23 10:25, 20 October 2022 (UTC)
In German elementary school we learned the a:b notation. When we learned more complex divisions in secondary school it was with the "scientist" notation. And as I am a software engineer AND (presumably) a normal person I use in general the respective notations. Elektrizikekswerk (talk) 07:24, 20 October 2022 (UTC)

For me, the version on the xkcd website has an additional line ("A/B: Software Engineer") that's not on this site. I think the comic might have been updated. Is anyone else seeing that? JBYoshi (talk) 23:20, 19 October 2022 (UTC)

Updated. Natg19 (talk) 00:31, 20 October 2022 (UTC)

For the Unicode one, I think it’s a reference to ⁄ (U+2044, fraction slash) or characters like ½, ¼, etc. - Cherryblossom (talk) 00:24, 20 October 2022 (UTC)

Is it important to note that 1/2 auctocorrects to ½ in many text-based programs like Microsoft Word?--Theunlucky (talk) 02:32, 20 October 2022 (UTC)

It's possible to use fraction-style notation in LaTeX by using \frac, or am I missing something?--162.158.2.125 05:49, 20 October 2022 (UTC)

"the long division symbol is only used in some countries". Only English-speaking ones, to be more precise. Most of the countries of the world use a different notation. 172.68.51.80 06:19, 20 October 2022 (UTC)

In the UK, the 'long division symbol' is nowadays often referred to (particularly with Primary classes, children aged 4 - 11) as the "Bus Stop Method". Because it looks like a UK bus shelter. MarquisOfCarrabass (talk) 07:07, 20 October 2022 (UTC)

I always used (still use, on the rare occasions that I do it) the notation inverted - B)_A - so that the answer is output beneath the problem, which makes more sense to me, given that we generally read down the page. I guess that would be a vandalised bus stop?172.70.162.147 09:16, 20 October 2022 (UTC)
When doing long-division, the intermediary sums (the calculated 'integer remainders' subtractions of progressively high-to-low powers of ten) would be done below in the 'standard' long-multiplication/addig/subtraction direction. The answer-figure is progressively created by the 'carry'-inverse to these more normal-looking arithmatic. Or so I surmise. Haven't used long-division, much, in 40 years or so (except in a polynomial-factoring thing, occasionally, using an extended version of the principle upon powers-of-whatever) so I might have the wrong-idea as to why the answer goes high (in that the non-answer that nevertheless leads to the answer goes low). ;) 162.158.159.29 16:17, 20 October 2022 (UTC)
For me, the remainders go in small figures above the next integer, so that they basically form a new number to divide.172.70.86.48 08:27, 24 October 2022 (UTC)

As a Dutch primary schoolchild, I have used a÷b for calculations and "a over b" for fractions (e.g. ⅘). For more difficult divisions, like what is 785/35, we used Staartdelingen (nl), long division, of which the primary notation is 35/735\. I think in early highschool we started using a over b for more complex calculations, "like (x+3) over 5 = 2, what is x". I had up to this XKCD never seen B⟌A, and would confuse it for what we use as square root symbol (√). IIVQ (talk) 07:16, 20 October 2022 (UTC)

Come to think of it, it's kind of odd that we used ":" for division. Why are there this many different division notations anyway? Same for multiplication. There's x, *, ⋅, x but centered vertically, and concatenation (for letter variables)!
The : operator is for ratios, where a:b could be a/b or b/a, but also metaphors, where a:b::c:d means a is to b as c is to d. 162.158.166.73 09:05, 20 October 2022 (UTC)

In Austria, school children are using the "scientist" notation from this comic. 172.68.50.51 08:17, 20 October 2022 (UTC)

Same thing in Russia 172.71.98.97 08:46, 20 October 2022 (UTC)

I live in Denmark, and “÷” seems to be often used here for subtraction, instead of a minus sign! Got confused a few times. nicolas (talk) 08:52, 20 October 2022 (UTC)

Also from DK and have often seen ÷ used as % and on my keyboard as I type this there is a ÷ on the number part of the keyboard to the right. But when I push it I get this: "/" In school we used this A:B to mean A/B, just as in Poland as mentioned above. Today I would write 10/2 not 10:2 or 10÷2. But I never used the last version. --Kynde (talk) 19:08, 23 October 2022 (UTC)
tableau
tab·leau /ˌtaˈblō/ noun
a group of models or motionless figures representing a scene from a story or from history; a tableau vivant. "in the first act the action is presented in a series of tableaux"

I don't think it means what the editor including it thinks it means. 172.69.22.185 09:02, 20 October 2022 (UTC)

"A graphic description or representation" - https://www.merriam-webster.com/dictionary/tableau
It derives from the idea of 'things set out on a table'. The arrangement of cards in a solitaire game is also called a tableau. 172.70.162.147 09:24, 20 October 2022 (UTC)
changed to radices. 172.70.206.93 10:18, 20 October 2022 (UTC)
Well that's not right, is it? - "the pungent usually crisp root of a widely cultivated Eurasian plant (Raphanus sativus) of the mustard family usually eaten raw"... 172.71.178.13 13:22, 20 October 2022 (UTC)
Naw... A radish is "like, almost 'rad', man, but not quite!", while "radices" are totally cool freezer-food!

The discussion of matrices and commutative rings is off topic. The comic is clearly about scalars alone. Please! 172.69.134.17 20:46, 20 October 2022 (UTC)

I thought it seemed on topic given the joke and demographic, but I think it could be presented better. 172.70.110.231 02:07, 21 October 2022 (UTC)

i type it as seen in 2 (counting the 2 schoolchilds as 1) and write it by hand as seen in 3 --an user who has no account yet 172.68.134.21 (talk) 15:05, 2 September 2023 (please sign your comments with ~~~~)